Eamcet - Maths - Binomial Theorem

If |x|

A.  r. 2r

B.  (2r-1)2r

C.  r. 22r+1

D.  (2r+1) 2r

(2r+1) 2<sup>r</sup>

Explanation :
No Explanation available for this question

If nεN, n is odd then n(n2-1) is divisible by

A.  24

B.  64

C.  17

D.  676

24

Explanation :
No Explanation available for this question

If the middle term of (1+x)2n is 1.3.5...(2n-1)k/n! then k=

A.  (3x)n+1

B.  (2x)n+1

C.  (2x)n

D.  (3x)n

(2x)n

Explanation :
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The general term of (2a-3b)-1/2 is

A.  1.3..5.....(2r-5)/r! 1/√2a(3b/4a)r

B.  1.3..5.....(2r-5)/r! 1/√2(3b/4a)r

C.  1.3..5.....(2r-5)/r! 1/2a(3b/4a)r

D.  none

1.3..5.....(2r-5)/r! 1/2a(3b/4a)r

Explanation :
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The coefficient of xr in (1+x)2/(1-2x)3 is

A.  2r(9r2+15r+8)

B.  2r-2(r2+9r+15)

C.  2r-3(9r2+15r+8)

D.  none

2r-3(9r2+15r+8)

Explanation :
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49n+16n+k is divisible by 64 for n?N. Then the numerically least –ve integer value of k is

A.  -2

B.  -1

C.  -3

D.  -4

-1

Explanation :
No Explanation available for this question

The coefficient of xr (0

A.  nCr(3r-2n)

B.  nCr(3n-r-2n-r)

C.  nCr(3r+2n-r)

D.  none

nCr(3n-r-2n-r)

Explanation :
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nC0+nC1+nC2+………+nCn =

A.  nn

B.  n!

C.  2n

D.  2n!

2n

Explanation :
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If the 5th term is 24 times the 3rd term in the expansion of (1+x)11 then x=

A.  ±4

B.  ±2

C.  ±3

D.  ±8

±2

Explanation :
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If Tr+1 is the term independent of x in (3x-5/x3)8 then r=

A.  1

B.  2

C.  3

D.  4

2

Explanation :
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The 4th term of (1-2x)-1 when x=1/3 is

A.  7/24

B.  8/27

C.  9/32

D.  11/45

8/27

Explanation :
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If xr occurs in the expansion (x+1/x2)2n, then its coefficient is:

A.  2nC(2n-r)

B.  2nC2n/3

C.  2nC(2n-r)/3

D.  none

2nC(2n-r)/3

Explanation :
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The sum of the coefficients of (1+2x-4x2)35 is

A.  0

B.  1

C.  -1

D.  2

-1

Explanation :
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The number of non zero terms in the expansion of (x+a)100 + (x-a)100 is

A.  100

B.  51

C.  201

D.  202

51

Explanation :
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If (3 + 4i) is a root of x2+px+q=0, then (p, q) is:

A.  (6, 25)

B.  (-6, -7)

C.  (6, 1)

D.  (-6, 25)

(-6, 25)

Explanation :
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The term independent of x in the expansion of (1+x+2x3)(3x2/2-1/3x/)9 is

A.  1/3

B.  1/4

C.  17/54

D.  19/54

17/54

Explanation :
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The number of terms in the expansion of (a+b+c+d)5 is

A.  20

B.  120

C.  336

D.  56

56

Explanation :
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The coefficient of x2 in1+x2/(1-x)3 is

A.  3

B.  4

C.  7

D.  12

7

Explanation :
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If p and q are the coefficients of xn in (1+x)2n-1 and (1+x)2n respectively then 2p=

A.  q

B.  2

C.  1

D.  3

q

Explanation :
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C0+C1/2+C3/3+ …………Cn/n+1+ =

A.  2n+1-1/n+1

B.  2n-1/n+1

C.  2n/n+1

D.  1/n+1

2n+1-1/n+1

Explanation :
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The positive integer which is just greater than (1+0.0001)10000 is

A.  3

B.  4

C.  5

D.  6

3

Explanation :
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The coefficient of x10 in 1-2x+3x2/1-x is

A.  1

B.  2

C.  3

D.  -2

2

Explanation :
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C1/1 – C2/2 + C3/3 – C4/4 +………. +(-1)n-1 Cn/n =

A.  1+1/2+1/3+....1/n

B.  1+1/2-1/3+....1/n

C.  1+2/3+3/4+....n/n+1

D.  none

1+1/2+1/3+....1/n

Explanation :
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The coefficient of x5 in the expression of (1+x)21+(1+x)22+……+(1+x)30 is

A.  51C5

B.  9C5

C.  31C6-21C6

D.  30C5+20C5

31C6-21C6

Explanation :
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The coefficient of x7 in (ax2-1/bx)11  is equal to the coefficient of x-7 in (ax-1/bx2) then ab=

A.  0

B.  1

C.  -1

D.  2

-1

Explanation :
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The number of non zero terms in the expansion of (8+2)101 - (8-2)101 is

A.  101

B.  50

C.  51

D.  204

51

Explanation :
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The coefficients of three consecutive terms in the expansion of (1+x)n are in the ratio 1:7:42, then n=

A.  55

B.   60

C.  72

D.  63

55

Explanation :
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Which term of (2x-3y)12 when x=1, y=5/2 numerically greatest?

A.  7

B.  8

C.  9

D.  11

11

Explanation :
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If two consecutive terms in the expansion of (x+a)n are equal where n is a positive integer then (n+1)a/x+a is

A.  a positive integer

B.  a negative integer

C.  an even integer

D.  an odd integer

a positive integer

Explanation :
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If the sum of odd terms and the sum of even terms in the expansion of (x+a)n are p and q respectively then p2+q2=

A.  (x2+a2)n

B.  (x2-a2)n

C.  1/2[(x+a)2n+(x-a)2n]

D.  1/2[(x+a)2n-(x-a)2n]